In the past few years, there are a lot of work on calculating the conductivities based on several holographic models. One conventional approach is that take the perturbation on the boundary by a time-dependent field with frequency \(\omega \)  to get the optical conductivities, and then take the zero frequency limit to get the DC conductivities. However, because of the translation invariance of the gravitational theories, there is the divergence in obtaining the DC conductivities. To avoid this unphysical diverge conductivities, one can introduce the linear axion field in the gravitational background to brake the spatial translation invariance but remain the homogeneous [1]}. In this gravitational model, the presence of the linear axion field results the momentum dissipation in the dual boundary theory. This model has been widely used in applied holographic calculations, see the reviews [2]} and therein.
